Presentations of Graph Braid Groups

Abstract

Let G be a graph. The (unlabeled) configuration space of n points on G is the space of all n-element subsets of G. The fundamental group of such a configuration space is called a graph braid group. We use a version of discrete Morse theory to compute presentations of all graph braid groups, for all finite connected graphs G and all natural numbers n.

27 pages, 11 figures

References in corpus (3)

• Abrams's stable equivalence for graph braid groups
• Braid groups and right angled Artin groups
• Braid Groups of the Sun Graph

Cited by in corpus (16)

• n-particle quantum statistics on graphs
• Non-abelian Quantum Statistics on Graphs
• Abrams's stable equivalence for graph braid groups
• Stability phenomena in the homology of tree braid groups
• Geometric presentations of braid groups for particles on a graph
• Computing braid groups of graphs with applications to robot motion planning
• Non-abelian anyons on graphs from presentations of graph braid groups
• Novel quantum phases on graphs using abelian gauge theory
• Topological complexity of unordered configuration spaces of certain graphs
• Totally normal cellular stratified spaces and applications to the configuration space of graphs
• Embeddings of right-angled Artin groups
• Configuration Spaces for the Working Undergraduate
• An algorithmic discrete gradient field and the cohomology algebra of configuration spaces of two points on complete graphs
• Graph of groups decompositions of graph braid groups
• Heisenberg homology of ribbon graphs
• Discrete homotopy of token configurations